Question

There are four primary strategies for determining the area of two-dimensional figures and shapes: a) counting square units, b) subdividing the shape into pieces, finding the areas of the pieces and adding the areas together, c) enclosing the shape in a rectangle, finding the area outside of the shape but inside the rectangle and subtracting, and d) using a formula. Explain each strategy. Use an example for each.

Answer 1

Given below

Explanation:

a) if we look at the picture then we can find by counting the square units. In each box there are 3.5 square units along the breadth. There are 3 square units along the length . Counting these gives (3*3.5= 10.5 ) 10.5 square units for each box. Adding the 10.5 +10.5+10.5+10.5 = 42 square units gives the area of the inner rectangle.

b) There are 4 boxes and the total area of the these boxes will be 4*10.5= 42 square units.

Area of 1 box = 3*3.5= 10.5

c) The area of the outer rectangle = 8*12= 96 square units.

The area between the two rectangles along the breadth = 3*7= 21 of one side.

The area between the two sides along the length = 6*1= 6 square units.

Subtracting 21+21+6+6= 54 from 96 gives 42 square units

d) Area= length *breadth

= 6* 7= 42 square units.

Hence by all four methods the total area remains the same.